Question

Which set of ordered pairs does not represent a function?

A. { (3, –2), (–2, 3), (4, –1), (–1, 4) }
B. { (3, –2), (3, –4), (4, –1), (4, –3) }
C. { (3, –2), (4, 3), (5, –4), (6, –5) }
D. { (3, –2), (6, –2), (9, –2), (12, –2) }

Answer 1

B. { (3, –2), (3, –4), (4, –1), (4, –3) }

Explanation:

Functions are a set of points that show how dependent variables change through independent variables.

Defining a Function

In functions, each x-value is assigned to exactly one y-value. This means that x-values do not repeat. So, if there is one x-value more than once in a set, then it cannot be a function.

For example, set B has the x-value 3 and 4 repeated twice. Thus, it does not represent a function.

Graph of a Function

Functions can also be defined through a graph. Just like with coordinate points, x-values do not repeat on the graph. You can use the vertical line test to see if a graph is a function. If you can draw a vertical line at every point on a graph without it ever intersecting with the graph more than once, then it is a function.